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s2008m [1.1K]
3 years ago
7

Which r-value represents the weakest correlation? –0.75 –0.27 0.11 0.54

Mathematics
1 answer:
Anit [1.1K]3 years ago
8 0

Answer:

0.11

Step-by-step explanation:

Strongest correlation:

The strongest correlations happen for r = -1 and r = 1, that is, when r has the higher absolute value.

In this question:

The value of r with the lowest correlation is the one with the lowest absolute value(absolute value of -0.75 is 0.75 for example), so it is 0.11, which is the answer.

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Does the following infinite series converge or diverge? 1/3+2/9+4/27+8/81+...
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Note that A and D are ludicrous choices, so you can throw them away outright. (Any divergent series cannot have a sum, and any convergent series must have a sum.)

The sum is certainly convergent because it can be written as a geometric sum with common ratio between terms that is less than 1 in absolute value.

S=\dfrac13+\dfrac29+\dfrac4{27}+\dfrac8{81}+\cdots
S=\dfrac13\left(1+\dfrac23+\dfrac{2^2}{3^2}+\dfrac{2^3}{3^3}+\cdots\right)

We can then find the exact value of the sum:

\dfrac23S=\dfrac13\left(\dfrac23+\dfrac{2^2}{3^2}+\dfrac{2^3}{3^3}+\dfrac{2^4}{3^4}+\cdots\right)

\impliesS-\dfrac23S=\dfrac13
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So the answer is B.
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